How do I import my Hair emission particles with my object into another blender project?
Importing to Other 3d Packages
If you're importing the object with hair into another program (3d package / game engine etc.) most likely you will want to convert the hair particles into real objects, see How can I convert a hair-particle system into 3D, editable objects? Note that particles won't be available for tweaking like particles because they won't be particles, rather than meshes.  

Importing to Blender New Projects
If you want only to import object with particles into another Blender project then just import it as object with standard Link / Append operators (enter Objects folder while browsing main .blend file); modifiers will be imported as well along with the particle system.